PROBLEMS OF GEOCOSMOS

In the Fig. 2, a the results of 1D interpretation of ρ a using program SVD and MEL are shown. The
model represents a 7-layer section (a black line). The number of data ρ a was 20 values per a decade of
square root of Т (in logarithmic scale). The regularization parameter was α = 0,005 , the number of iteration
iter = 15 , discrepancy rms = 0,01 . It is necessary to notice, that the algorithm of program MEL is
constructed on Backus and Gilbert method (Backus and Gilbert, 1967) which is a special case of method
SVD. Program MEL is one of the successful programs 1D inversion (Porokhova and Kharlamov, 1990). In
the Fig. 2, b the results of modeling in the presence of 20% of noise and corresponding confidence intervals
are given.
a b
Resistivity, Ohm m
10000
1000
100
10
1
model
mel
svd
svd (minimum of layers)
0.1 1 10 100 1000
Depth, km
Resistivity, Ohm.m
10000
1000
100
10
1
0.1 1 10 100 1000
Depth, km
Fig.2. Results of 1D interpretation of ρ a : a) the comparison of program SVD and MEL; b) the result of interpretation
(red line) - in the presence of noise (20 %) in data, black lines - boundaries of confidence intervals.
In the Fig. 3 it is shown the dependence of 1D interpretation on the number of model layers and periods. It
can be seen that the optimal variant is 10 layers per a decade of depths and 5 values per a decade of square
root of T (in logarithmic scale). In the figure these values are noted by the asterisk.
Resistivity, Ohm.m
Proceedings of the 7th International Conference "Problems of Geocosmos" (St. Petersburg, Russia, 26-30 May 2008)
10000
1000
100
10
1
a b
1 Depth (km)
20
*10
5
10
0.1 1 10 100 1000
Depth, km
327
Resistivity (Ohm.m)
10000
1000
100
10
1
1 sqrt [Period(s)]
20
10
*5*
2,5
10
minimum of Periods
1 2 5 10 s
0.1 1 10 100 1000
Depth (km)